Quantum Mechanics (GATE Physics): Questions 1 - 3 of 35

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Question number: 1

» Quantum Mechanics » Angular Momentum and Spin

Appeared in Year: 2014

Short Answer Question▾

Write in Short

A hydrogen atom is in the state ψ=821ψ20037ψ310+421ψ321

Where n,l,m in ψnlm denote the principal, orbital and magnetic quantum numbers, respectively. If L is the angular momentum operator, the average value of L2 is________ 2 .

Question number: 2

» Quantum Mechanics » Time-Independent Perturbation Theory

Appeared in Year: 2014

MCQ▾

Question

A particle is confined to a one dimensional potential box with the potential

V(x)={0,0<x<a,otherwise

If the particle is subjected to a perturbation, within the box, W=βx , where β is a small constant, the first order correction to the ground state energy is –

Choices

Choice (4) Response

a.

0

b.

αβ2

c.

αβ4

d.

αβ

Question number: 3

» Quantum Mechanics » One, Two and Three-Dimensional Potential Problems

Appeared in Year: 2015

MCQ▾

Question

The average energy U of a one dimensional quantum oscillator of frequency ω and in contact with a heat bath at temperature T is given by,

Choices

Choice (4) Response

a.

U=12ωcosh(12βω)

b.

U=12ωsinh(12βω)

c.

U=12ωtanh(12βω)

d.

U=12ωcoth(12βω)

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